A Math Nerd's Guide to Slicing Pizza

In a new paper, mathematicians have figured out new techniques to segment a pie equally.

For me, pizza is often the solution to a stressful day. For a math wiz, however, a pie can serve a very different purpose: it’s a problem waiting to be solved.

There’s a growing body of pizza-related mathematical research. Dr. Eugenia Cheng, for instance, came up with the formula for the perfect pie. A mathematician duo at Louisiana State University figured out how pizza that was sliced off-center would be distributed among two buddies. And as WIRED’s Aatish Bhatiaexplains, the work of 19th century genius Carl Friedrich Gauss underlies the fold-first-and-then-stuff-in-your-mouth technique most of us employ while consuming that greasy New York slice. Now, a new paper by two mathematicians at the University of Liverpool adds to this incredibly important knowledge: it posits new and intricate ways to divide up a pie in equal proportions.

In this paper, the authors are concerned with a geometrical arrangement called “monohedral tiling,” in which all tiles within a larger geometrical form are “congruent to each other,” write authors Joel Haddley and Stephen Worsley in the paper. In other words, the tiles are all the same shape. Here’s how the authors explain the aim of their research:

We will investigate the possibility of producing monohedral tilings of the disk. Such tilings are produced on a daily basis by pizza chefs by taking radial cuts distributed evenly around the centre of the pizza.

Mathematicians already knew from previous research that they can divide the six congruent slices of the pizza, cut through the center of the pie (below, left) by dividing each slice across its middle.The result is twelve three-sided slices, six on the inside with very little crust, and six on the outside with the most of the crust (below, right):

But the slicing patterns Haddley and Worsley have designed in their new paper go beyond 3-sided slices. The mathematicians show that, theoretically, pies can be sliced into segments with any number of odd sides, like so:

The same is true for slices with these weird, jagged edges:

The implications of the results are, er, sort of limited to the field of geometry, but they do encourage Instagram-worthy photos of strangely-sliced pizza pie.

“I’ve no idea whether there are any applications at all to our work outside of pizza-cutting,” Haddley tells theNew Scientist. But the results are “interesting mathematically, and you can produce some nice pictures,” he adds, referring to this photo of a pie sliced up as per his new technique:

About the Author

Tanvi Misra is a staff writer for CityLab covering immigrant communities, housing, economic inequality, and culture. She also authors Navigator, a weekly newsletter for urban explorers (subscribe here). Her work also appears in The Atlantic, NPR, and BBC.